Preheat oven to 375 degrees. Place chicken breast halves in a 9x13 baking dish; bake, uncovered, for 10 minutes. Meanwhile, heat the olive oil in a large skillet over medium-high heat; saute mushrooms, onion and garlic until mushrooms begin to turn brown, about 8-10 minutes. Remove from heat. Add mustard, capers, vinegar, hot sauce and mayonnaise to skillet. Mix together and spread the mixture over the chicken. Continue to bake until chicken is no longer pink in the center, about 20-25 minutes longer.